# hw1 - devices Most people probably would not object to own...

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ECE 440 Homework I Spring 2006 Due: Wednesday, January 25, 2006 1. How many atoms are found inside a unit cell of a simple cubic (sc), body-centered cubic (bcc), face-centered cubic (fcc), diamond structure, and zinc-blende structure crystal? Find the maximum fractions of the unit cell volume that can be filled by hard sphere in the sc, bcc, fcc and diamond lattices. If all unit cells have the same lattice constants, i.e. the unit cell dimension, which structure among sc, bcc, fcc, diamond and zincbelnde has the largest atomic density (atoms/cm 3 )? Which of them has the highest packing density, i.e. highest volume fraction being occupied by hard spheres? 2. Beginning with a sketch of a fcc lattice, add atoms at (1/4, 1/4, 1/4) from each fcc atom to obtain the diamond lattice. Show that only four added atoms in Fig. 1-8a appear in the diamond unit cell. How many nearest-neighbor atoms does each atom have in a diamond structure? 3. Gold is commonly evaporated in vacuum to fabricate electrical contacts of semiconductor
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Unformatted text preview: devices. Most people probably would not object to own one or two pieces of gold treasure. It never hurts to know a little bit about gold. A thin gold foil is 10 cm square and 5 mils in thickness. (one mil is one thousandth of an inch.) The mass of the foil is found to be 24.51 g. (a) Determine the inter-atomic distance (in angstrom) between two nearest-neighbor gold atoms. Note that gold is in an FCC structure. (b) Hypothetically, a phase transformation takes place and the original gold foil transforms from FCC to a crystal structure like silicon. Assume that the “new” gold foil is still 10cm x 10cm. How thick would be the new gold foil (in centimeter)? Assume that the nearest-neighbor distance of gold does not change after transformation. What would be the foil thickness if instead the lattice constant remains the same before and after transformation?...
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